this is worrisome. i've just stated my main theorem, and already i have 8 slides. to my credit, however, one of the slides is a title page, another is a diagram, and two others are full of references.

so perhaps i'm doing well:

after 3 slides (which includes stating someone else's theorem), i can state mine.

odd: lecturing is a little like running. with enough teaching experience, one knows one's own pace. [1] accounting for gory computations and careful diagrams, 6-7 handwritten pages of my notes usually fills a 50-minute lecture.

then again, i may cover material more quickly than others. possibly i am slower: i don't know. you'd have to ask my students.

speaking of students, yesterday a student visited my office hours. usually this is a time to be tactful, to lecture less, and in particular, to make sure that i'm not doing all the work that students should be doing [2].

i was expecting a statement like:

"

*i don't know how to do #23.*

can you show it to me?"

can you show it to me?

instead, the student asked:

"

*i really don't understand what a subspace is and what a basis is.*

can you explain it again?"

can you explain it again?

so we talked about subspaces and bases, and various levels of concrete or abstract examples. (s)he asked good clarifying questions -- "

*what about this? does that check that it's a basis?*" -- i like to think that the student now understands these fundamental notions better, but i can't be sure.

well, at least it was more fun than my usual office hour questions.

**(:**

[1]

*my cadence is disturbingly regular: 160-165 steps per minute (counting footsteps of both feet), which i think is relatively normal. i've been told that elite runners have a cadence of around 185-190 steps a minute.*

[2]

*when i think about it, there is much less effort in doing the problem for the students rather than urging them along and make them do it themselves. it may well be easier; however, are the students really learning if they don't do it themselves?*

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